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There are insanely many tsumego in existence, but many of them are very artificial and would never occur in real games. While any tsumego helps to improve, specifically learning shapes likely to be encountered in actual games would be of great benefit. I'm especially thinking of fast games with little time to actually read.

Are there any collections of problems that are likely to occur in real games, or at least close to it?

Get Strong at Life and Death starts with a section on standard shapes. The second part of the book contains problems arising from joseki and joseki variations. This is an advanced book - aimed at dan-level players.

I'll second TimK's suggestion of Life and Death, particularly for developing a general approach, and also throw in a few others I've found useful:

The Korean Problem Academy is an excellent collection of progressively more difficult problems. The books themselves are the best way to go if you can find them, as they have no answer key but generally can be solved relatively quickly and with patterns that show up in actual games.

Rescue and Capture by Yang YiLun is not really about L&D per se, but there's a strong related element in finding tesuji to rescue or capture groups. You can still find this book over on Yutopian.

SmartGo has a wide mix of problems, many of which fit with what you are looking for.

For speed games in particular I'm partial to the advice that you should find the level of problem that you can solve "almost instantly" since what you are doing is training speed reading and pattern recognition. This means that you may end up doing problems that are "below you rank," but that's an excellent way to be able to actually see and solve the problems in game.